Trajectories, computational fluid dynamics

Particle trajectories can be calculated by utilizing the modern CFD (computational fluid dynamics) methods. In these calculations, the flow field is determined with numerical means, and particle motion is modeled by combining a deterministic component with a stochastic component caused by the air turbulence. This technique is probably an effective means for solving particle collection in complicated cleaning systems. Computers and computational techniques are being developed at a fast pace, and one can expect that practical computer programs for solving particle collection in electrostatic precipitators will become available in the future. 

FIGURE 13.9 Bubble trajectories of gas from the side spargers (left picture, v = 0.8 m/s) and middle spargers (right picture, v = 2.5 m/s) comparison computational fluid dynamic (CFD) prediction (lines) and tracer experiments (dots or diamonds) [20]. Reprinted with permission from from [32]. Copyright (2006) Elsevier. 

Computational fluid dynamic simulations have been nsed to model the drop/partiele trajectories in spray-drying (Gianfrancesco et al., 2010), but optimization is still complex. 

FIGURE 12.9 Typical particle trajectory using an axial flow impeller (A310) with 100 am particles using computational fluid dynamics. 

Chapter 5 of Volume 1 described in detail how the flow patterns of hot air and the trajectories of the drying droplets can be analyzed by computational fluid dynamics... 

The gas flow pattern in cyclones is fairly well known from experimental evidence collected over decades. For particle trajectories, on the other hand, very little experimental data are available, so for this we shall resort to computational fluid dynamics (CFD) simulations. 

Monte Carlo methods offer a useful alternative to Molecular Dynamics techniques for the study of the equilibrium structure and properties, including phase behavior, of complex fluids. This is especially true of systems that exhibit a broad spectrum of characteristic relaxation times in such systems, the computational demands required to generate a long trajectory using Molecular Dynamics methods can be prohibitively large. In a fluid consisting of long chain molecules, for example, Monte Carlo techniques can now be used with confidence to determine thermodynamic properties, provided appropriate techniques are employed. 

Computer simulations such as that described above can afford abundant information on structural and dynamic properties of fluid systems. Here we focus attention on the trajectory diagram of the solution. Figure 3 shows 10 picosecond trajectories for the molecules in a layer of 20 A x 20 A x 3.3 A. This is one of six layers which are produced by dividing the cubic cell. Incidentally this layer contains two TBA molecules indicated by shading for illustration. 

Classical Dynamics of Nonequilibrium Processes in Fluids Integrating the Classical Equations of Motion Control of Microworld Chemical and Physical Processes Mixed Quantum-Classical Methods Multiphoton Excitation Non-adiabatic Derivative Couplings Photochemistry Rates of Chemical Reactions Reactive Scattering of Polyatomic Molecules Spectroscopy Computational Methods State to State Reactive Scattering Statistical Adiabatic Channel Models Time-dependent Multiconfigurational Hartree Method Trajectory Simulations of Molecular Collisions Classical Treatment Transition State Theory Unimolecular Reaction Dynamics Valence Bond Curve Crossing Models Vibrational Energy Level Calculations Vibronic Dynamics in Polyatomic Molecules Wave Packets. 

A few theoretical and computational studies have already addressed in some detail the problem of viscosity in ILs.[136] However, a complete microscopic theory of viscosity is currently not available. It is a challenging task to accurately compute the viscosity of a complex system by means of simulation methods. For a system with high viscosity, it is extremely difficult to reach the hydrodynamic limit (zero wave number) where the experimental data is observed. This is because, in order to reach this limit, a very large simulation box is required. Traditional simulation methods normally used for shear viscosity of fluids fall into two categories (a) the evaluation of the transverse-current autocorrelation function (TCAC) through equilibrium molecular dynamics (HMD) trajectories and (b) non-equilibrium molecular dynamics (NEMD) simulations that impose a periodic perturbation. [137] In recent work, Hess[138] compared most of the above methods by performing simulations of Lermard-Jones and water system. They concluded that the NEMD method using a periodic shear perturbation can be the best option. 

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